The two main ingredients in the derivation of this result are Poincaré symmetry and the ansatz (REF ). Poincaré is assumed to be an exact symmetry of the scattering problem, uncorrected by loops or effective field theory operators. On the other hand, the ansatz (REF ) relies on a tree-level argument, which can receive corrections. For example, in gauge theories with massless matter, the ansatz should exhibit a branch cut extending from \(z = 0\)  to reproduce the loop corrections in momentum space that are known to appear at every order in perturbation theory [1]}, [2]}. In particular, the singularity structure at one-loop includes terms of the form \(\sim \frac{1}{z} \log z\) .
